Is it permissible to distribute Zakat funds to the beneficiaries monthly instead of paying them in one lump sum, knowing that the reason for the installments is to ensure continued benefit throughout the year and to meet emergency needs?

It is obligatory to pay the entire zakat to its eligible recipients at the time it becomes due. It is not permissible to pay it in installments under the pretext that the recipient will spend it all and then be in need later. Separating zakat money and holding onto it does not relieve one of this obligation; rather, it is obligatory to pay it to its eligible recipient to clear one's liability.